Subtleties in AdS$_2$/CFT$_1$

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I was looking at few papers on AdS$_2$/CFT$_1$. It seems to me that this is not as well studied as the higher dimensional dualities (e.g, AdS$_3$/CFT$_2$ or AdS$_5$/CFT$_4$). Can someone summarize what the actual difficulties are. For example, I have some related questions in this setup.

1. How to define a CFT$_1$? Is it just quantum mechanics with conformal invariance?

2. How to define central charge of CFT$_1$? What will be its physical meaning (like degrees of freedom, anomaly or Casimir energy)?

3. I came across the statement that AdS$_2$ is not stable by itself. One needs to have electric flux to make it stable. Why/how is it so? And if it is true then what is its analog in the dual CFT$_1$?

(If someone wishes to answer this, please feel free to discuss other subtleties related to AdS$_2$/CFT$_1$ .)

This post imported from StackExchange Physics at 2016-09-05 19:39 (UTC), posted by SE-user Physics Moron

Could you please give references to one or two of the papers you had looked at?

Well, here is one : arxiv.org/abs/hep-th/9812073 Summarizing this paper briefly will be a great answer to my question actually. :-)

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